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We identify some situations where mappings related to left centralizers, derivations and generalized -derivations are free actions on semiprime rings. We show that for a left centralizer, or a derivation , of a semiprime ring the mapping defined by for all is a free action. We also show that for a generalized -derivation of a semiprime ring with associated -derivation a dependent element of is also a dependent element of Furthermore, we prove that for a centralizer and...
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